As a first note, I think it would be helpful to understand the morphology of these third-declension neuter nouns in -ma as they appear in Greek:
Nominative ὄνομᾰ ὀνόμᾰτᾰ
Genitive ὀνόμᾰτος ὀνομάτων
Dative ὀνόμᾰτῐ ὀνομάσῐ(ν)
Accusative ὄνομᾰ ὀνόμᾰτᾰ
Vocative ὄνομᾰ ὀνόμᾰτᾰ
As you can see, the standard formation is ὀνομάσῐ(ν) [onomasi(n)]. Of all the forms above, this is the only one that does not have an immediately handy Latin morphological transcription (or near-transcription, as in the genitive singular and plural). The question then becomes: what dative/ablative form should they use instead?
In its entry for poema, L&S marks poematis as the "usual" form, quoting Cicero and Plautus:
quod idem in poematis, in picturis usu venit in aliisque compluribus (Cic. Off. 3.15)
nam neque fictum usquamst neque pictum neque scriptum in poematis
ubi lena bene agat cum quiquam amante, quae frugi esse volt. (Plaut. As. 1, 3, 22)
It also cites Suetonius as an example of poematibus. Besides the "usually," it does not give additional helpful information.
Usage numbers for poematis/-ibus
A search of the Packhum corpus (keeping in mind that genitives must be excluded) reveals that Plautus uses poematis (dat.) once, Varro (2nd-1st century BC) 3 times, Cicero 4 times, and Gellius (2nd century AD) numerous times.
A similar search for poematibus returns only 5 results, including 1 from Varro, 1 from Pliny the Elder (see below--this is probably a point for poematis), 1 from Suetonius (1st-2nd AD), 1 from Apuleius (2nd AD), and 1 from Pomponius Porphyrion (2nd AD).
Conclusion: poematibus is significantly rarer and has only one attestation from the Golden Age, whereas poematis has been used since Plautus and exists concurrently (even in the same author!). Significantly, Cicero only uses -is.
Maurius Servius Honoratus (4th-5th century AD) mentions the dative and ablative of neuter words specifically as an exception to normal Greek declension of borrowed words, citing Cicero as his authority. He does not even acknowledge the possibility of -ibus:
sed haec maiores nostri aut tertia declinatione declinabant, si fuissent generis neutri, ut poema poematis; aut prima declinatione declinabant, si fuissent generis feminini, ut haec poema huius poemae. quamquam invenimus aliquos casus nec ab illis nec ab istis regulis declinatos, id est genetivum pluralem et dativum et ablativum plurales: legimus enim apud Ciceronem horum poematorum his poematis et ab his poematis; similiter et emblematorum et emblematis, peripetasmatorum peripetasmatis. (Honoratus, Commentarius in Artem Donati, 435.8-13)
In Pliny the Elder's (1st century AD) Dubius Sermo 83,84, the fragments seem to show him explicitly rejecting the "more correct" -ibus in favor of this usage:
quamquam ab 'hoc poemate' 'his poematibus' facere debeat, tamen consuetudini et suavitati aurium censet Varro summam esse tribuendam.... [break]
...quam maxime vicina Graeco Graece dicit uti ne 'schematis' quidem dicat, sed
(The text of the fragment in question is here: feel free to correct if I am misinterpreting. The facere debeat...tamen juxtaposition, though, seems fairly convincing that he is recommending the usage of -is.)
My conclusion: poematis is a safer bet, even if neither is incorrect.